[dctoedt]

The Christian sect known as "Shakers" illustrate what you describe: They had a rule of celibacy and as a result have essentially died out; their Wikipedia entry says that as of 2021 their total membership was three people.

https://en.wikipedia.org/wiki/Shakers

[midoridensha]

Unless those 3 people (and those in recent decades who have now died) were hypocrites and broke the rules, then the only way the sect has survived this long is immigration (we'd call it "converts" in this context, since they're not a country). However, while it's kept them alive since the 1800s, 3 people is pathetically small.